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What would be an ideal system through which amateurs can advertise their results?

Occasionally on MathOverflow (and elsewhere on and off the internet), amateur mathematicians try to advertise their research results and solicit feedback from professionals. For example, recently HH Hannett (who holds a long-ago BS in mathematics, but has been doing non-math engineering work for many years) asked a well-meaning but inappropriate-for-the-forum question about Where to submit a recent paper, and how to cope with the negative or dismissive responses received from a previous journal submission. In a comment on a subsequent (now-deleted) post, Hannett wished “that there might be a mechanism whereby amateur (“non-PhD”) contributions can get a fair shake …. Perhaps some sort of delegated, tiered system that a paper has to survive.”

Discussing whether/what/how such a system should exist/be like/be set up is, to my mind, valuable. A potential answer is that the existing peer-review process is already adequate. I could certainly believe that the best answer is “no change necessary”: I’m young enough that I don’t really know the full extent of the current system; maybe we should just continue to avoid the cranks. But most amateurs don’t want to waste professionals’ time — they want to do math, and for the same reason (it’s fun!) that professionals do, and the current academic system, clearly, does not provide sufficient outlets for well-meaning amateurs (or “cranks” wouldn’t be a problem).

My hope with this post, then, is to constructively generate some ideas for relieving this pressure. In particular, it’s all well and good to ask that amateurs learn and follow reasonable advice, but my goal is to come up with things that professionals can do (pro)actively. These ideas could range from the fantastical (design a better peer-review system! establish free universal advanced mathematics education!) to the specific (make “respond to amateurs” part of universities’ “service” requirements!). An important note: My goal is not to establish yet another thread in which we can swap stories of all the dumb things amateurs have sent us. That’s certainly a fun game, but there are other outlets for it.

So, netizens: What, specifically, are the weaknesses and strengths of the current system when it comes to amateur mathematics? What would
be an ideal system through which amateur mathematicians could advertise their work and solicit feedback? How can professional
mathematicians help to set up such a system?

(this is an addendum by Ben)

Maybe I should save this for the comments, but I can’t resist abusing my blog privileges and throwing out an idea. I don’t think that any system that require a lot of input from people on the usual professional mathematics track is likely to succeed; it’s hard enough to get them to seriously read each other’s papers (for example, I’d much rather see a system whereby graduate students can read and give feedback on each other’s papers than one where they read amateur mathematicians). But perhaps we can ask amateurs to review each other’s work.

One could have a website where anyone can upload preprints and then give people function to vote on the preprints, write reviews and vote on the reviews. The power of your vote could be regulated using a page-rank type system where you only get real voting power as other people vote up your work. This wouldn’t have to restricted to amateurs only, but it’s hard for me to imagine it catching on quickly with professionals. Of course, it’s hard to know whether it would attract a big enough and diverse enough user base to effectively sort through papers, but you never know, it might.

10 thoughts on “What would be an ideal system through which amateurs can advertise their results?”

I’d like to point out that there *already exists* a website where anyone can upload preprints, called the arXiv :-)

Adding everything else that Ben asks for in a “wrapper” website is of course something doable. It takes a bunch of someone’s time to set up, but it’s not like it’s a hard thing to do these days.

This suffers from the usual problem, however — such a website isn’t much use until sufficiently many people are actively using it, and it’s unclear how to get from here to there.

The solution, I think is to come up with something that is *immediately* useful (and hopefully something that’s really easy to implement), and for which there is a clear sequence of additional features and (hopefully) enlargements of the user base that reach the endpoint we’re after. (Heck, let’s be fantastical, and aim for a whole new journal and peer review system, but in baby steps.)

I even have a proposal!

The arxiv RSS feeds are not nearly as useful as they could be. For one, if you subscribe to multiple categories you receive multiple copies of crossposted articles. Also, there aren’t feeds for any finer divisions than arxiv categories — no feeds for custom searches, for example.

It would be pretty easy to solve this. Set up a simple website, that lets you click some checkboxes, maybe fill in some search fields, etc., and it gives you a custom URL providing an RSS feed of exactly the slice of the arxiv you want. Such a website could be created in an afternoon by a few people who know what they’re doing, and it would be immediately useful.

Can we get from such a website to something more like what Ben is talking about? Well yes! It would be easy to let users mark various papers as interesting or excellent, and it would be easy to make this information public, and incorporate it into other people’s feeds. Lots of my colleagues are better and more enthusiastic readers of papers than I am, and if, for example, I could get an RSS feed of every paper that Noah read and thought was great, I’d be really happy!

There are a couple more fairly obvious incremental improvements that could be made, and I’ll leave it as an exercise to the reader to decide if this could eventually reach the state of providing a distributed, accountable, *useful* system of “peer review”.

There are already news groups for this kind of exchange, so it is not a new idea. And the amateurs keep posting their results there, but the problem is professionals don’t like to spend time reading them.

About the proposed ideas, the main problem is that most amateurs are not interested in helping or don’t know enough math to do it, so they just someone to read their paper and confirm it. And any system needs to deal with this problem. A possible solution would be allowing them to review each others papers and give feedback and based on the feedback the owner of the paper will give some points to the reader, so they will have incentives to read each others papers and write short reviews on them.

I think one problem here is that people does not seem to understand that time is important, more important than money. Asking us to read amateur papers is like asking chemists working in big medical corporations to read amateur medicine designs for an HIV cure. Because doing math does not need people spend money but only their time, we have way more math amateurs trying to solve open math problems than there are amateurs people trying to find a cure for HIV or cancer, and because they spend their time writing their results they expect others to spend professional to spend their time. Is it solving an open problem in math easier than finding a cure for HIV or coming up with a new drug? No! the only reason we get such attention from amateurs is that math only needs a pen and a pencil and time, and they don’t understand that other people’s time is valuable, i.e. it is cheap hobby for them but not for us.

With regards to comment 1., I have been thinking for some time that a website linked to the arXiv allowing people to make comments on and ask questions about papers could be very valuable, both for readers and authors, perhaps even more valuable than all but the best referee report. Extrapolating from my own habits, I guess that an enormous amount of energy gets spent on understanding and annotating interesting papers. So it could be very efficient If there were some organized means to cooperate and communicate while reading papers.

I used to be concerned that it would be difficult to maintain a decent level of civility on such a website, but I think MO has shown that incivility concerning mathematics is relatively rare.

As for the original question about amateur mathematics, I think it is worth remembering that there is a spectrum of professional mathematicians, from those who build enormous theories to prove enormous theorems to those who work on relatively simple problems that could be understood by undergraduates. I would guess that there are already outlets for the latter kind of work and that a good amateur might fit in there. (Here relatively simple means the amount of machinery that is involved in approaching the problem, not how difficult the problem is to solve.)

I think that Chris’ idea (comment No 3) about public paper annotations is marvelous!

To some extend, it would also help amateur mathematicians, since it provides a general framework for “judging” papers and it doesn’t make a difference whether it’s an article by a professional mathematician or by an amateur.

Why not simply start with what is there in arxiv, references and users. Each current user of arxiv, i.e. email address, is assigned points dependent upon the number of references to their papers (Such points could be divided equally among co-authors.). In other words, as a first cut simply steal the PageRank algorithm with some slight modifications to disallow, for example, self-references giving points.

This has the obvious advantage of not requiring any work from anyone, save the person who actually writes the wrapper around arxiv. Also, the members of arxiv would automatically be members of the wrapper site and have reputation points without having to do anything except login. So, we immediately have many knowledgable users.

Users submitting to arxiv would automatically submit to the wrapper site; where as, amateurs could submit to the wrapper site and maybe later get promoted to be allowed to submit to arxiv at some number of reputation points.

Maybe, in addition to references giving points, we could also have a MO-like point system layered on top of the PageRank system. User A could transfer reputation points of theirs, i.e. vote up, a paper Z by user B, and this would give user B more reputation points without requiring user A to write a paper referencing paper Z. When doing so, user A could also comment on the paper.

I completely agree with comment 3. If widely used, it would be much more efficient than peer-review.
I considered at some point making such a website. The big problem is, as it has already been said, to get enough people to use it in order to make it useful.
Here is a great and free comment engine with all the features required (comment rating, reputation points for authors, etc…).http://intensedebate.com/

FWIW, I (a professional programmer only getting started in Mathematics) had thoughts on something very similar to this[1]. The basic idea was to have a “formalised” system for entry of proof-steps, upon which a complete proof could be built (online), and then each step would be validated via some rule system (by analysing the context of the step, i.e. “Let X be a set of …”, (leveraging existings tools), or via a linking-structure that the proof author would establish (this relys on that, for this, etc).

The idea being that an entire proof could be built, and each component could be analysed. If a fault lay in a particular area, it could be represented visually, and you’d get to see which part of the proof falls down, or which segment of a certain section is left out.

On the link it may be possible to view the wiki where the thoughts are contained, but it may not (due to firewall restrictions at a given workplace).

I’ve begun work on the idea, but left it by the wayside recently due to other projects. If anyone feels that it is a particularly fruitful idea, I’d be more than happy to work on it again, with anyone who was so inclined (Otherwise, I’ll probably get around to it when the time suits, or the occasion demands).

I think the thing most people, amateur and professional, share is a desire to see more good mathematics getting done. Suggestions that have the ability to directly raise the quality of amateur mathematics are going to get to the heart of the problem – the frustration that amateurs experience from feeling shut out, and the fact that professionals feel like their time is wasted by interacting with amateurs.

Looking at another field that has to cope with enthusiastic, undertrained amateurs, there are scads of writing MFA programs structured around the fact that their students have to have full-time jobs to support themselves while they pursue writing as a side love. Is something like that kind of program possible for research math? There might be enough demand in a few towns (for example, San Francisco or Boston) to support a kind of “night degree” – one that would explicitly not be a steppingstone to a career in academia.

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